BUSI 230 HW 5.2 The Addition Rule and the Rule of Complements Assignment solutions complete answers
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The General Addition Rule states that .
If events A and B are mutually exclusive, then .
Given an event A, the event that A does not occur is called the of .
The Rule of Complements states that .
If P(A)=0.46, P(B)=0.7, and P(A and B)=0.4, find P(A or B).
If P(A)=0.6, P(B)=0.3, and A and B are mutually exclusive, find P(A or B).
If P(A)=0.46, P(B)=0.7, and P(A or B)=0.4 are A and B mutually exclusive?
If P(B)=0.2, find P(B^c).
Determine whether events A and B are mutually exclusive.
A red die and a blue die are rolled.
A: The red die comes up 5.
B: The total is 4.
A: Jayden has a math class on Tuesdays at 2:00
B: Jayden has an English class on Wednesdays at 2:00
A sample of 300 phone batteries was selected. Find the complements of the following events.
(a)More than 233 of the batteries were defective.
(b)At least 233 of the batteries were defective.
(c)Fewer than 233 of the batteries were defective.
(d)Exactly 233 of the batteries were defective.
Car repairs: Let E be the event that a new car requires engine work under warranty and let T be the event that the car requires transmission work under warranty. Suppose that P(E)=0.1, P(T)=0.09, P(E and T)=0.02.
(a) Find the probability that the car needs work on either the engine, the transmission, or both.
(b) Find the probability that the car needs no work on the engine.
(b) Find the probability that the car needs no work on the transmission.
Computer purchases: Out of 812 large purchases made at a computer retailer, 349 were personal computers, 396 were laptop computers, and 67 were printers. As a part of an audit, one purchase record is sampled at random. Round the answers to four decimal places, as needed.
(a) What is the probability that it is a tablet?
(b) What is the probability that it is not a laptop computer?
Visit your local library: On a recent Saturday, a total of 1351 people visited a local library. Of these people, 254 were under age 10, 165 were aged 10-18, 152 were aged 19-30, and the rest were more than 30 years old. One person is sampled at random.
(a) What is the probability that the person is less than 19 years old? Round your answer to four decimal places.
(b) What is the probability that the person is more than 18 years old? Round your answer to four decimal places.
Weight and cholesterol: The National Health Examination Survey reported that in a sample of 13136 adults, 6305 had high cholesterol (total cholesterol above 200 mg/dL), 8407 were overweight (body mass index above 25), and 3941 were both overweight and had high cholesterol. A person is chosen at random from this study. Round all answers to four decimal places.
(a)Find the probability that the person is overweight.
The probability that the person is overweight is .
(b)Find the probability that the person has high cholesterol.
The probability that the person has high cholesterol is .
(c)Find the probability that the person does not have high cholesterol.
The probability that the person does not have high cholesterol is .
(d)Find the probability that the person is overweight or has high cholesterol.
The probability that the person is overweight or has high cholesterol is .
